Abstract: Let{(X_n,Y_n)} be i.i.d. random vectors with common d.f. F. Under weaker conditions, it is shown in this paper that A_n^-1(Y_{(n, n)}-B_n)→I holds for some nondecreasing function I. Therefore the Nagaraja and David's result is generalized. Moreover, We prove that our conditions are not only sufficient, but also necessary for weak convergence of the sequence (a_n^-1(X_{n, n}-b_n), A_n^-1(Y_{(n, n)}-B_n)). At last, we show that the weak convergences of bivariate extreme values and (a_n^-1 (X_{n, n}-b_n), A_n^-1(Y_{(n, n)}-B_n)) are closely related.

Key words: induced maximum, weak convergence for distribution functions, bivariate extremes

摘要： 设{(X_n,Y_n)}是i.i.d.随机向量序列，共同d.f.为F。本文在更弱的条件下证明了A_n^-1(Y_{(n, n)}-B_n)→I对某准d.f.I成立，从而推广了Nagaraja和David的结果。此外还指出：对于(a_n^-1(X_{n, n}-b_n),A_n^-1(Y_{(n, n)}-B_n))的联合分布的弱收敛，本文的条件不仅充分，而且必要。最后，揭露了二元极值弱收敛与(a_n^-1 (X_{n, n}-b_n), A_n^-1 (Y_{(n, n)}-B_n))的联合分布弱收敛之间的紧密联系。

关键词: 伴随极值, 分布函数的弱收敛, 二元极值